If 20 men or 24 women or 40 boys can do a job in 12 days working for 8

Hi...
Let's count in terms of men..
1 w = 20/24 m.....b = 1/2 m..
So if 20 m can do a work in 12*8 H, 20*12*8 m will do it in 1 h..
4 times the work will require 12*8*4*20 m..
Working 5*12 per man , \(\frac{20*12*8*4}{5*12}=128m\)
But 6w and 2b are also there.. 6w=6*20/24=5m....2b=2*1/2=1m..
So remaining men required=128-5-1=122

D

20 men work for 12 days for 8 hours to do a job
so number of men required to complete the work in 12 days working 5 hours = (20*8)/5 =32
as the work is 4 times as big as the previous one, so no of men required will be = 4*32 = 128
Now we already have 6 women and 2 boys. we need to convert them to men to find the remaining no of men required

24W=20M, or 6W=(20*6)/24 = 5 Men

40B=20M, or 2B = (20*2)/40 = 1 Men

So number of men required = 128-(5+1) = 122

Option D

This solution is short and clear..
I am trying to figure out how (20*8)/5 =32..
Is there a formula for this?

Hi pclawong
as 12 days are constant for both the scenarios, let's not think about it.
20 men take 8 hours to complete the job
No of men required if work is done only for 1 hour a day = 8*20 men(more men as hours worked are less)
No of men required if work is done for 5 hours a day = (8*20)/5 (less men required now)

The solution above stems from the basics

Work = number of labor * Rate * Time

Because it is same work

W1 = W2

n1 * R1 * T1 = n2 * R2 * T2 ( in this case, R1 = R2, so cancel out as each man have same rate)

n1 * T1 = n2 * T2

From men's work numbers, apply in equation above

20 * 8 * 12 = n2 * 5 * 12

n2 = 20 * 8 / 5 ...............same result as described in previous post.

I hope it helps

We can let the job = 1, and we are given that the job can be completed in 12 x 8 = 96 hours by 20 men or 24 women or 40 boys. Let’s determine the rate of 1 man per hour, which is (1/20)/96 = 1/(20 x 96). Similarly, the rate of 1 woman per hour is (1/24)/96 = 1/(24 x 96) and the rate of 1 boy per hour is (1/40)/96 = 1/(40 x 96).

Now we are given that another job is four times as big, and thus this new job = 4. We also are given that 6 women, 2 boys, and some number of men will be working on this job for 5 x 12 = 60 hours. We need to determine the number of men needed. We can let the number of men needed = n and create the following equation:

6 * 1/(24 x 96) * 60 + 2 * 1/(40 x 96) * 60 + n * 1/(20 x 96) * 60 = 4

360/(24 x 96) + 120/(40 x 96) + 60n/(20 x 96) = 4

Multiplying the entire equation by 96, we have:

360/24 + 120/40 + 60n/20 = 384

15 + 3 + 3n = 384

3n = 366

n = 122

Answer: D

We know the daily rate of:

A) Man is 1/(20*12*8) = 1/1920
B) Woman is 1/2304
C) Boy is 1/3840

So, 1 man equals to 2 boys and 6 women produce as much as 5 men.

So, we want to know how many men should we add to the 6 men (6 women plus 2 boys).

Now, we know that 20 men need to work 1920 hours to complete one job, working 8h/day for 12 days.

Since the second job is 4 times as big as the first one, it will need 1920*4 = 7680 hours from men.

So, we should divide that amount of hours per 60 hours (the amount of hours each person can work in the second job, as in, 5h/day x 12 days).

We'll have: 7680/60 = 128 men.

So, we need 128 men in total. But since we already have 6 women and 2 boys already working (or 6 men), there will be 128-122 men working alongside them.

Since 20 men/24 women/40 boys can complete the piece of work, working 8 hours a day for 12 days
we can assume the total work to be 20 * 8 * 12 units.

20 men:24 women:40 boys will translate to 1 man:1.2 woman:2 boys

We need to the find the total number of men working to complete a work 4 times as large working for 12 days at 5 hours/day.

If the number of men needed to complete 4*(20*8*12) units of work at 5*12 is x, we can calculate x as \(\frac{4*(20*8*12)}{5*12} = 128\)

Now, we are told that 6 women and 2 boys will be helping the man complete the work.
They would effectively do \(\frac{6}{1.2} + \frac{2}{2}\) or 5 + 1 = 6 men's work respectively.


Therefore, the total men needed to complete the work along with 5 women and 2 boys is 128 - 6 = 122(Option D)

Let a be the number of men.

Given, \(8*12*20m = 8*12*24w = 8*12*40b\)
\(5m = 6w = 10b\)

\((6w + 2b + a.m) = 4*8*12*24w\)

\(6 + a = 128\)
\(a = 122\)

r=w/t

20m=1/12*8, m=1/12*8*20
24w=1/12*8, w=1/12*8*24
40b=1/12*8, b=1/12*8*40

20m=24w=40b; m=2b
xm+6w+2b=4/5*12, x(2b)+6w+2b=1/15,
2b(x+1)+6w=1, [30b](x+1)+[90w]=1,
[30b]…[30*(1/12*8*40)]…3/12,8,4…1/16*8
[90w]…[90*(1/12*8*24)]…30/12,8,8…5/16*8
[1/16*8](x+1)+[5/16*8]=1, x+1+5=16*8,
x=128-6=122

Ans (D)

So here's the thing.
>20 men work 12 days for 8 hours to complete a job.
~ So, Each of men are doing (12*8)= 96 hours of work
~ So it takes total (20*96) = 1920 hours of work

> Now the questions ask for a work, which is 4 times bigger than the previous one.
~ So, It will take (1920*4)= 7680 hours of work.

Cool!

Now, If only men are work for this job, how many of them will be needed?
~ So, before going that calculation, I need to know how many hours that each of the men will work?
~ So, Working will be 5 hours a day for 12 days, which concludes (12*5) = 60 hours of work will need to be done by each man.

> So there are total 7680 hours of work
~ So the total number of men will work is (7680/60)= 128 men.

Now,
I have 6 women and 2 boys already for that job, so if I interchange them with men it will be (6 women= 5 men) and (2 boys= 1 man), so, I already have 6 men.
> So I only need (128-6)= 122 men for the job.
Answer: (D) 122.

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